Perturbative conformal symmetry and dilaton

Spontaneous symmetry breaking with necessity leads to the presence of Goldstone field(s). In the case of scale or conformal symmetries the corresponding Goldstone mode is called the dilaton. Consistently coupling a system to the dilaton poses certain difficulties, for the trace of the energy momentum tensor may not necessary be zero, which in turn leads to the dilaton acquiring a mass. In this paper we present the approach allowing perturbatively to keep the dilaton massless, i.e. to preserve conformal symmetry, at any fixed order in perturbation theory.

Figure 1

One- and two-loop UV divergent topologies and their leading divergence. (a) $O({ϵ}^{-1})$, (b) $O({ϵ}^{-2})$, (c) $O({ϵ}^{-2})$, (d) $O({ϵ}^{-1})$.